Algebra Flashcards
What is the expression for an odd number?
2a+1 where a is an integer.
What is the expression for an even number?
2b where b is an integer.
What is proof by deduction?
Proof by deduction is using known facts to show a statement must be true.
What is a rational number?
A number that can be written as the quotient of two integers. (A quotient is a result obtained by dividing one quantity by another.)
What is proof by exhaustion?
You break the statement down into two or more cases where these cases cover all possible situations. Then prove the statement is true for each case.
What is disproof by counter-example?
When you show a mathematical statement is false by finding one case where the statement doesn’t hold.
How do you expand brackets?
Times every term in one bracket by every term in the other. A term outside the brackets must be multiplied by every term inside.
How do you factorise an expression?
If there is a common factor between every term you can divide each term by it and put the factor outside brackets with the new expression in it.
What is the difference of two squares?
a^2-b^2 = (a-b)(a+b)
What do fractions need in order to be added or taken away?
A common denominator.
How can algebraic fractions be simplified?
If a factor appears in both the numerator and denominator they can be cancelled.
What are the laws of indices?
a^m*a^n = a^(m+n) a^m/a^n = a^(m-n) (a^m)^n = a^(mn) a^1 = a a^(1/m) = (m)route(a) a^-m = 1/a^m a^(m/n) = (n)route(a^m) = ((n)route(a))^m a^0 = 1
What are the laws of surds?
(2)route(ab)= (2)route(a)(2)route(b)
(2)route(a/b) = (2)route(a)/(2)route(b)
a = ((2)route(a))^2 = (2)route(a)(2)route(a)
((2)route(a) - (2)route(b))((2)route(a) + (2)route(b)) = a-b
How do you rationalise the denominator?
Multiply top and bottom of the fraction by an expression that will get rid of the surds in the denominator. If the denominator is in the form a + (2)route(b) multiply by a - (2)route(b).
